Details

Time bar (total: 5.8s)

sample35.0ms

Algorithm
intervals
Results
14.0ms280×body80valid
5.0ms112×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0246646
1890606
23702588
35001584

prune282.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.5b

localize116.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.4b
(/ (* a c) b)
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
19.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0459640
12217559
25001554

prune325.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.7b

localize123.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
59×times-frac
38×*-un-lft-identity
34×add-cube-cbrt
33×add-exp-log
25×associate-*r*
22×associate-*l*
21×add-cbrt-cube
16×sqrt-prod
12×unpow-prod-down div-exp unswap-sqr
9×prod-exp
8×add-log-exp
7×pow1
6×cbrt-undiv sqr-pow
5×cbrt-unprod
3×associate-/r* div-inv
2×pow-to-exp flip3-- sqrt-div pow-exp sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 136
Calls
4 calls:
45.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
31.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
09181365
146041210
250021167

prune649.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.7b

localize127.0ms

Local error

Found 4 expressions with local error:

4.4b
(cbrt (/ c (pow b 1/2)))
4.4b
(cbrt (/ c (pow b 1/2)))
4.4b
(cbrt (/ c (pow b 1/2)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
75×cbrt-prod
63×times-frac
48×add-sqr-sqrt
47×add-cube-cbrt *-un-lft-identity
27×unpow-prod-down
9×sqr-pow
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 117
Calls
4 calls:
3.0ms
(cbrt (/ c (pow b 1/2)))
3.0ms
(cbrt (/ c (pow b 1/2)))
3.0ms
(cbrt (/ c (pow b 1/2)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series474.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (/ c (pow b 1/2)))
130.0ms
(cbrt (/ c (pow b 1/2)))
135.0ms
(cbrt (/ c (pow b 1/2)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03311091
110931062
250011055

prune758.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.7b

regimes164.0ms

Accuracy

93.5% (0.9b remaining)

Error of 7.7b against oracle of 6.7b and baseline of 21.1b

bsearch340.0ms

Steps
ItersRangePoint
9
2.6683347110001497e+63
3.895668027475672e+69
3.688339606012e+69
10
-2.0369510893777665e-297
3.098498077083345e-307
-1.0787310192989e-310
9
-3.6963232668708646e+158
-3.0922224130316533e+150
-1.3459740091915103e+154

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
068110
17155
27455
37455

end0.0ms

sample831.0ms

Algorithm
intervals
Results
445.0ms8714×body80valid
136.0ms2903×body80nan